If you are trying to get into the 338 LM game as inexpensively as possible, you might do better by purchasing a Savage FCP in 338 LP for around $1,200 or so. I hear they are shooters and generally hold to .75 MOA or less.

You get the action, 20 MOA rail, a decent stock and a decent barrel. If you like the 338 LM game (it can be expensive), then you can begin to upgrade from there. I am currently pulling parts together for a 338 LM AI build. More than once I have cried about the money involved and have been tempted to sell off my parts and buy an FCP.

I have a Stiller TAC-338 for this build and I believe you are correct in that it is the least expensive action you can get for a custom build. You may be able to find a gunsmith willing to make a single shot 338 LM for you based on a Rem 700 mag action, but fewer and fewer are willing to do so.

Best bang for the buck... I'd start with the Savage 110 FCP. Mine shoots .50 M.O.A or better... using 300gr Berger OTM, 89.3gr of RETUMBO and.. Lapua brass... of course ;) ... I find that the berger's like a jump somewhere around 70 thousandths in this action.